2018/01/22 by Huimin Liu, Liu, Huimin, Xueke Pu +1
Mathematics · Physics and Astronomy · #35M20 #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35M20 #msc:35Q35
paper · pdf · doi:10.48550/arxiv.1801.07601
37 pages. arXiv admin note: text overlap with arXiv:1602.08016 by other authors
openalex publication_date 2018/01/22 · openalex created_date 2018/02/02 · arxiv created 2019/08/05 · arxiv updated 2019/08/07 · openalex updated_date 2026/07/28
The nonlinear Schrödinger (NLS) equation can be derived as a formal approximation equation describing the envelopes of slowly modulated spatially and temporarily oscillating wave packet-like solutions to the ion Euler-Poisson equation. In this paper, we rigorously justify such approximation by giving error estimates in Sobolev norms between exact solutions of the ion Euler-Poisson system and the formal approximation obtained via the NLS equation. The justification consists of several difficulties such as the resonances and loss of regularity, due to the quasilinearity of the problem. These difficulties are overcome by introducing normal form transformation and cutoff functions and carefully constructed energy functional of the equation.